Both leaders, speaking at the opening of the U.N. General Assembly, agreed the United Nations should authorize a multinational peacekeeping force and that other nations help rebuild Iraq, now controlled by a U.S.-led coalition.
In his speech, Bush said the United States was working on a new Iraq resolution that will "expand the U.N.'s role in Iraq. As in the aftermath of other conflicts, the United Nations should assist in developing a constitution, training civil servants, and conducting free and fair elections."
It was the first gathering of world leaders at the U.N. General Assembly since the United States invaded Iraq and ousted Saddam Hussein. Also at the meeting was Ahmad Chalabi, the current president of the U.S.-appointed Iraqi Governing Council, who took Iraq's seat in the General Assembly.
Bush faced a skeptical audience. The U.S.-led war caused deep splits at the United Nations, and the new U.S. draft resolution has brought a debate over handling the post-war transition. France has said it wants power handed over to the Iraqis in a matter of months -- a stance backed by Germany's chancellor on Tuesday.
CBS News Correspondent Lou Miliano reports countries will privately fume at the president's request. Publicly, they will be supportive — with strings attached.
Secretary-General Kofi Annan opened the debate Tuesday with a criticism of Bush's "pre-emptive" attack on Iraq.
Such strikes "could set precedents that result in a proliferation of the unilateral and lawless use of force, with or without credible justification," Annan said. He underlined that the world should collectively address the threats that prompt pre-emptive action — terrorism and weapons of mass destruction.
But Annan also urged world leaders to set aside their disputes over the war and join forces to build a peaceful democracy in Iraq.
Bush, speaking with Chirac in the audience, insisted the timetable for handing over power to the Iraqis must be "neither hurried nor delayed by the wishes of other parties."
"This process must unfold according to the needs of Iraqis," he said.
His speech was greeted by polite applause, while Chirac's soon after his garnered a warmer response.
Chirac said the transition process need to be conducted "according to a realistic timetable," and that the United Nations could "help the Iraqis draft a constitution and hold elections."
"In Iraq, the transfer of sovereignty to the Iraqis, who must have sole responsibility for their future, is essential for stability and reconstruction," Chirac said.
Chirac has said his country will not veto the planned U.S. resolution on Iraq.
Bush left the assembly meeting after his speech and before Chirac took the podium. Later, the two leaders met privately outside the U.N. building. At a news conference Chirac held immediately following, he emphasized "a deep friendship that exists between France and the United States," even when they disagree on issues.
Earlier, as leaders streamed into U.N. headquarters, Annan held a series of meetings, including one with German Chancellor Gerhard Schroeder, who told reporters that he wanted to see power handed over to the Iraqi people in a "matter of months."
It was Schroeder's most specific comments yet on a timetable and echoed the French position for a swift hand-over of power to the Iraqis. Previously Schroeder had said Berlin would like to see the transfer take place "as quickly as possible."
In his address, Chirac insisted the right to use force can only come from the U.N. Security Council.
"No one should be able to accord himself the right to use (force) unilaterally and preventatively," an advance copy of Chirac's speech said.
"In an open world, no one can isolate themselves, no one can act alone in the name of all and no one can accept the anarchy of a society without rules," he said. "There is no alternative but the United Nations."
Last year, Bush came to the General Assembly to challenge its member states to confront the "grave and gathering danger" of Saddam Hussein's Iraq — or stand aside as the United States acted alone.
In the months that followed, France, Germany, Russia and others opposed the war and were incensed when the United States attacked Iraq without Security Council approval.
This year, with mounting bills and U.S. casualties, Bush wants help from the United Nations and support for a U.S.-backed resolution that Washington hopes will encourage countries to contribute troops and money.
France, Germany and Russia want a larger U.N. political role and a much quicker transfer of power to the Iraqis than Washington is prepared to accept.
The key U.N. meeting comes after devastating bomb attacks against its headquarters in Baghdad in the past month have plunged the world body into mourning and raised questions about its future role.
"Subject to security considerations, the United Nations system is prepared to play its full part in working for a satisfactory outcome in Iraq, and to do so as part of an effort by the whole international community," Annan said.
He called on member states to address the expansion of the Security Council — an issue that has gone nowhere for a decade — and urged the council to deal effectively with the most difficult issues. Response to massive killings and rights abuses in Congo and Liberia this year had been "hesitant and tardy," he said.
Annan sent letters to world leaders ahead of this week's meeting, challenging them to come up with new ideas to deal with wars, terrorism, poverty and other threats to international security.